Optimization is Not Enough: Why Problem Formulation Deserves Equal Attention

2026-02-05

AI Summary

This work addresses the limitations of black-box optimization in structural design, which often yields suboptimal or physically implausible solutions due to its neglect of problem modeling and domain knowledge. Focusing on the topology optimization of laminated composite structures, the study proposes an explicit decoupling of topological and fiber orientation design variables, combined with a physics-informed sequential optimization strategy. This approach departs from conventional context-agnostic black-box paradigms by leveraging domain-specific insights. Compared to concurrent optimization of all variables, the proposed sequential method significantly improves compliance minimization under volume constraints, yielding superior and physically interpretable designs. The results underscore the critical role of integrating domain knowledge into the optimization process to enhance both performance and solution plausibility.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Constraint Satisfaction and Optimization: Constraint Optimization
• Machine Learning: Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Black-box optimization is increasingly used in engineering design problems where simulation-based evaluations are costly and gradients are unavailable. In this context, the optimization community has largely analyzed algorithm performance in context-free setups, while not enough attention has been devoted to how problem formulation and domain knowledge may affect the optimization outcomes. We address this gap through a case study in the topology optimization of laminated composite structures, formulated as a black-box optimization problem. Specifically, we consider the design of a cantilever beam under a volume constraint, intending to minimize compliance while optimizing both the structural topology and fiber orientations. To assess the impact of problem formulation, we explicitly separate topology and material design variables and compare two strategies: a concurrent approach that optimizes all variables simultaneously without leveraging physical insight, and a sequential approach that optimizes variables of the same nature in stages. Our results show that context-agnostic strategies consistently lead to suboptimal or non-physical designs. In contrast, the sequential strategy yields better-performing and more interpretable solutions. These findings underscore the value of incorporating, when available, domain knowledge into the optimization process and motivate the development of new black-box benchmarks that reward physically informed and context-aware optimization strategies.

Problem

• black-box optimization
• problem formulation
• domain knowledge
• topology optimization
• composite structures

Innovation

• problem formulation
• black-box optimization
• domain knowledge
• sequential optimization
• topology optimization